$ -\dfrac{4}{6} \div \left(\dfrac{4}{7} \div \dfrac{4}{7}\right) = {?} $
Solution: First, we can simplify the problem: $ -\dfrac{2}{3} \div \left(\dfrac{4}{7} \div \dfrac{4}{7}\right) = {?} $ Dividing by a fraction is the same as multiply by the reciprocal of that fraction. $ = -\dfrac{2}{3} \div \left(\dfrac{4}{7} \times \dfrac{7}{4}\right) $ $ = -\dfrac{2}{3} \div \left(\dfrac{4 \times 7} {7 \times 4}\right) $ $ = -\dfrac{2}{3} \div \dfrac{28}{28} $ $ = -\dfrac{2}{3} \times \dfrac{28}{28} $ $ = \dfrac{-2 \times 28}{3 \times 28} $ $ = -\dfrac{56}{84}$ Simplify: $ = -\dfrac{2}{3}$